On a Conjecture of Nevai
نویسندگان
چکیده
It is shown that a conjecture concerning the derivatives of orthogonal polynomials, proved by Nevai in 1990 for generalized Jacobi weights, holds for doubling weights as well.
منابع مشابه
Critical Lieb-thirring Bounds in Gaps and the Generalized Nevai Conjecture for Finite Gap Jacobi Matrices
We prove bounds of the form ∑ e∈I∩σd(H ) dist ( e, σe(H ) )1/2 ≤ L-norm of a perturbation, where I is a gap. Included are gaps in continuum one-dimensional periodic Schrödinger operators and finite gap Jacobi matrices, where we get a generalized Nevai conjecture about an L1-condition implying a Szegő condition. One key is a general new form of the Birman-Schwinger bound in gaps.
متن کاملOn Erdélyi-magnus-nevai Conjecture for Jacobi Polynomials
T. Erdélyi, A.P. Magnus and P. Nevai conjectured that for α, β ≥ − 1 2 , the orthonormal Jacobi polynomials P (α,β) k (x) satisfy the inequality max x∈[−1,1] (1− x) 1 2 (1 + x) 1 2 ( P (α,β) k (x) )2 = O (
متن کاملFreud's Conjecture for Exponential Weights
exists. He expressed the value that the limit should take in terms of gamma functions, and proved his conjecture for a = 2,4,6. Recently, Al. Magnus [8] proved the conjecture for p > —1 and a a positive even integer, and subsequently [9] for weights of the form exp(—P(x)), where P(x) is a polynomial of even degree with positive leading coefficient. Maté, Nevai, and Zaslavsky [11] have sharpened...
متن کاملProbabilistic Averages of Jacobi Operators
I study the Lyapunov exponent and the integrated density of states for general Jacobi operators. The main result is that questions about these can be reduced to questions about ergodic Jacobi operators. I use this to show that for finite gap Jacobi operators, regularity implies that they are in the Cesàro–Nevai class, proving a conjecture of Barry Simon. Furthermore, I use this to study Jacobi ...
متن کاملOn some generalisations of Brown's conjecture
Let $P$ be a complex polynomial of the form $P(z)=zdisplaystyleprod_{k=1}^{n-1}(z-z_{k})$,where $|z_k|ge 1,1le kle n-1$ then $ P^prime(z)ne 0$. If $|z|
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014